1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/static/rex_fsle.ma".
16 include "static_2/i_static/rexs.ma".
18 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
20 (* Advanced properties ******************************************************)
22 lemma rexs_sym: ∀R. rex_fsge_compatible R →
23 (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
24 ∀T. symmetric … (rexs R T).
25 #R #H1R #H2R #T #L1 #L2 #H elim H -L2
26 /4 width=3 by rex_sym, rexs_step_sn, inj/
29 (* Main properties **********************************************************)
31 theorem rexs_trans: ∀R,T. Transitive … (rexs R T).
32 #R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)